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Improved bounds on coloring of graphs

✍ Scribed by Sokol Ndreca; Aldo Procacci; Benedetto Scoppola

Book ID: 113582451
Publisher: Elsevier Science
Year: 2012
Tongue: English
Weight: 280 KB
Volume: 33
Category: Article
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.12.002

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We show that for all large n, every n-uniform hypergraph with at most 0 7 n/ ln n × 2 n edges can be 2-colored. This makes progress on a problem of Erdős [Nordisk Mat. Tidskrift 11, 5-10 (1963)], improving the previous-best bound of n 1/3-o 1 × 2 n due to Beck [Discrete Math. 24, 127-137 (1978)]. We